Mathematical Modelling and Numerical Simulation of the On-line Structural Health Monitoring System

Abstract

To design a Structural Health Monitoring (SHM) system, it is important to understand phenomenologically and quantitatively the wave propagation in composite materials and the influence of the geometrical and mechanical properties of the structures. To accelerate the design of SHM systems, the fluid-structure interaction (FSI) effect on the wave propagation has to be considered. In this contribution, a concept of coupling FSI with an ultrasonic wave propagation is proposed, which is referred to as eXtended Fluid-Structure Interaction (eXFSI) problem. The eXFSI is a one-directional coupling of typical FSI problem with an ultrasonic wave propagation in fluid-solid and their interaction (WpFSI). The WpFSI is a strongly coupled problem of acoustic and elastic wave equations and automatically adopts the boundary and initial condition from previous time step. To the best of our knowledge, such a model is new in the literature. The FSI is modelled in terms of the arbitrary Lagrangian Eulerian (ALE) technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff (STVK) material model. The WpFSI problems are solved on the moving mesh which is automatically adopted from the FSI problem at each time step. The ALE approach provides a simple, but powerful procedure to couple solid deformations with fluid flows by a monolithic solution algorithm. However, Combining fluid dynamics with structural analysis traditionally poses a formidable challenge for even the most advanced numerical techniques due to the disconnected, domain-specific nature of analysis tools. The principal aim of this research is the exploration and development of concepts for the efficient numerical solution of the eXFSI problem. The finite element method is used for the spatial discretization. Temporal discretization is based on finite differences and is formulated as a one step- scheme, from which we can consider shifted Crank-Nicolson and the fractional-step- schemes. The nonlinear problem is solved by a Newton-like method. Our application of the eXFSI and WpFSI models is the design of on-line and off-line Structural Health Monitoring (SHM) systems for composite material and lightweight structure, respectively. The implementation is accomplished via the software library package DOPELIB.